Problem: Omar is 12 years younger than Christopher. For the last two years, Christopher and Omar have been going to the same school. Eight years ago, Christopher was 3 times older than Omar. How old is Christopher now?
Answer: We can use the given information to write down two equations that describe the ages of Christopher and Omar. Let Christopher's current age be $c$ and Omar's current age be $o$ The information in the first sentence can be expressed in the following equation: $c = o + 12$ Eight years ago, Christopher was $c - 8$ years old, and Omar was $o - 8$ years old. The information in the second sentence can be expressed in the following equation: $c - 8 = 3(o - 8)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $c$ , it might be easiest to solve our first equation for $o$ and substitute it into our second equation. Solving our first equation for $o$ , we get: $o = c - 12$ . Substituting this into our second equation, we get the equation: $c - 8 = 3($ $(c - 12)$ $ -$ $ 8)$ which combines the information about $c$ from both of our original equations. Simplifying the right side of this equation, we get: $c - 8 = 3c - 60$ Solving for $c$ , we get: $2 c = 52$ $c = 26$.